You have probably seen distance-time graphs before, that look a bit like this example below:

But what about graphs like this? What do they represent?

This graph represents an object that is **accelerating. **Let's learn about acceleration, and how we use graphs to show this.

Acceleration is the **rate of change of speed**. If an object is accelerating, it is getting faster and faster over time. The greater the acceleration, the more the object speeds up per second.

A similar term is **deceleration. **If an object decelerates, that means that it is getting slower and slower over time.

We can show acceleration with a distance-time graph. Here is the example from before.

As you can see, the graph shows a **curve. **Curved lines on distance-time graphs show acceleration (or deceleration).

But why do curves show acceleration?

First, you might remember that the **gradient **(steepness) of a graph tells us the speed of the object.

In this example, object A and object B are both travelling at **constant speeds. **But object A is moving at a higher speed because it has a **steeper gradient. **

Look at the acceleration graph again. How does the gradient **change?**

The line gets **steeper and steeper **as time goes on. This must mean the object is getting faster and faster - it is accelerating!

What might a graph of a **decelerating **object look like?

In this graph, you can see that the line is getting **less steep **as time goes on - it is getting flatter. This means that the object is getting slower and slower, it is **decelerating.**

Now we are going to practise interpreting more distance-time graphs, and how to use them to make calculations.

Look carefully at the graph above.

In section A, the object is **accelerating.**

In section B, the object is **stationary.**

In section C, the object is moving at a **constant speed.**

In section D, the object is **decelerating **(and moving backwards).

What is the speed of the object in section C? Remember the equation for speed:

What is the distance travelled by the object, in section C? We can look at the y-axis to check.

The object starts section C at 6 metres and ends at 8 metres. So, it travels a distance of **2 metres.**

How much time did this take?

The object starts section C at 5 seconds and ends at 9 seconds. So, the time taken is 4 seconds.

What is the speed of the object during section C?

Speed (m/s) = Distance (m) ÷ Time (s)

Speed (m/s) = 2 m ÷ 4 s = 0.5 m/s

Now let's apply what we have learnt to some questions!